BGE Problem with Automated Door (Can't Pass Through)
The physics mesh for an object is created at game start, and is not updated based on animations. For some reason armatures, even if they move the whole object, don't seem to update the physics mesh

In this case, it would be easiest to make the elements of the door non-collision, and animate a separate object (eg a cube) that slides up and down to let the player in - without an armature.